Critics say the law could allow businesses to turn away gay and lesbian customers in the name of religious freedom. Indiana Gov. Mike Pence defended the law in a weekend appearance on ABC News' "This Week."
"The question here is if there is a government action or a law that an individual believes impinges on their religious liberty, they have the opportunity to go to court, just as the Religious Freedom and Reformation Act that Bill Clinton signed allowed them to go to court, and the court would evaluate the circumstance under the standards articulated in this act," Pence said.
Pence said he expects a clarification bill to be introduced in the coming week.
"We're not going to change the law," he said, "but if the general assembly in Indiana sends me a bill that adds a section that reiterates and amplifies and clarifies what the law really is and what it has been for the last 20 years, than I'm open to that."
Pence was adamant that the measure, slated to take effect in July, will stick.
"We're not going to change this law," he said.
The law quickly gained national attention after it was signed Thursday. The NCAA, which is based in Indianapolis, released a statement expressing concern that the law would negatively impact athletes and visitors in town for the Final Four games of its men's basketball tournament.
"The NCAA national office and our members are deeply committed to providing an inclusive environment for all our events," the NCAA said in a statement. "Moving forward, we intend to closely examine the implications of this bill and how it might affect future events as well as our workforce."
Final Four action begins Saturday at Lucas Oil Stadium in Indianapolis, and will feature Michigan State against Duke and Kentucky facing Wisconsin. The championship game follows on Monday, April 6.
"Discrimination in any form is unacceptable to me," Barkley said in a statement, expressing the belief that major sports events should not be held in the state.
"I've never been big into politics but I'm very disappointed in my adopted home state of Indiana and the passing of Senate Bill 101," Miller wrote in a social media post. "I've always been about inclusion for all, no matter your skin color, gender or sexual preference. ... We are all the same people, beautiful creatures."
The NBA and WNBA -- along with the Pacers and Fever franchises, which play home games in the state -- also issued a statement.
"The game of basketball is grounded in long established principles of inclusion and mutual respect. We will continue to ensure that all fans, players and employees feel welcome at all NBA and WNBA events in Indiana and elsewhere," the statement read.
The Twitter hashtag #boycottindiana drew viral attention in recent days, and figures such as Hillary Clinton called the law "sad." Internet giant Angie's List canceled a $40 million expansion project in Indiana.
"There's something very dangerous happening in states across the country," he wrote.
"These bills rationalize injustice by pretending to defend something many of us hold dear," Cook added. "They go against the very principles our nation was founded on, and they have the potential to undo decades of progress toward greater equality."
Organizers of at least two major conventions have also expressed concern. Adrian Swartout, the CEO of the 50,000-person Gen Con gamers' convention, said the measure could affect the group's decision to hold the major event in Indianapolis past 2020. He said it would have a "a direct negative impact on the state's economy."
Leaders of Disciples of Christ, a 400,000-person denomination based in Indianapolis, also said the situation could affect future commitments.
"We are particularly distressed at the thought that, should [the bill] be signed into law, some of our members and friends might not be welcome in Indiana businesses -- might experience legally sanctioned bias and rejection once so common on the basis of race," they said in the letter.
Supporters say discrimination concerns are overblown because the law -- which would take effect in July -- is modeled after a federal religious freedom law Congress passed in 1993 and similar laws are on the books in 19 states. However, the current political climate is far different than it was when most of those were approved because the U.S. Supreme Court is expected to rule this year on whether gay marriage bans violate the Constitution.
Conservative groups say the Indiana measure merely seeks to prevent the government from compelling people to provide such things as catering or photography for same-sex weddings or other activities they find objectionable on religious grounds.
Some business owners such as leather worker Casey Sampson say the law protects their religious beliefs.
"One example would be if someone came in here and wanted a belt that said, 'Satan is Great.' That is not something that we believe in," Sampson said.
The Associated Press contributed to this report.